Adsorption differential entropies

Fig. XVII-23. (a) Entropy enthalpy, and free energy of adsorption relative to the liquid state of N2 on Graphon at 78.3 K (From Ref. 89.) b) Differential entropies of adsorption of n-hexane on (1) 1700°C heat-treated Spheron 6, (2) 2800°C heat-treated, (3) 3000°C heat-treated, and (4) Sterling MT-1, 3100°C heat-treated. (From Ref 18.)...

In Fig. 5.21, from Dawson s paper, the uptake at X for the 250°C-outgassed sample is dose to the calculated value for a monolayer of water with a (H20) = 101 A. Point X has therefore been ascribed to a close-packed monolayer of water on a hydroxylated surface of rutile. The fact that the differential entropy of adsorption relative to the liquid state (calculated from the isosteric heat of adsorption) changes sharply from negative to positive values in this region with A s 0 at X was regarded as supporting evidence. ... 

Nagoe, M. Morimoto, T. (1969). Differential heat of adsorption and entropy of water absorbed on zinc oxide surface. Journal of Physical Chemistry, 73, 3809-14. 

Figure 13.13 Compensation relation between differential heat and differential entropy of adsorption.

We will illustrate the method by outlining the calculation of the (differential) entropy of adsorption. For S, we use the Sackur-Tetrode expression, Eq. (76) of Chapter 5, with a term added for the internal degrees of freedom ... 

Figure 4. Net differential entropy of adsorption of krypton on ground muscovite...

The differential entropy of adsorption can be readily calculated from the differential enthalpy of adsorption since from Equations (2.46), (2.51) and (2.54) we obtain ... 

The integration of the differential entropy of adsorption between 0 and T is conveniently carried out with the variables T, V and A held constant ... 

In the general case, the integral molar entropy of adsorption is not equal to the mean differential entropy of adsorption over the range of surface excess concentration from 0 to r, because of the extra term of the right-hand side of Equation (2.67). 

We can verify with Equation (2.68) that Aads/i<0 since, for physical adsorption, the equilibrium pressure necessary to obtain the surface excess concentration r (or n) increases with the adsorption temperature. It follows that A is necessarily negative. However, since the differential entropy of adsorption, at constant T, given by Equation (2.56) is directly proportional to the differential enthalpy of adsorption, its calculation is not of great value. 

Many systems give linear plots of pjn against p over a limited ranges of pressure, but such linearity does not by itself imply conformity with the Langmuir model. As already indicated, a second condition is that the energy of adsorption should be independent of surface coverage. Thirdly, the differential entropy of adsorption should vary in accordance with the ideal localized model (Everett, 1950). That no real system has been found to satisfy all these requirements is not surprising in view of the complexities noted here and in subsequent chapters. 

In summary, an attempt has been made in sections 5.2 and 5.3 to provide a number of formulations for the thermodynamic properties of surface phases. Special emphasis has been placed on the key role of the Gibbs adsorption equation as a link between the experimentally available isotherm data, and the determination of molar or differential entropies, enthalpies,... 

Substituting into Equations 6 and 7 the values of the derivative and A calculated from Equation 1, we obtained the following expressions for differential entropy and differential heat of adsorption (2) ... 

Summarizing, an attempt has been made to provide a systematic account of the thermodynamic properties of the adsorbed phase. The Gibbs adsorption equation, as an extension of the Clausius-Clapeyron equation, has played a key role in linking experimental isotherm data to the determination of molar or differential entropies and enthalpies. Similarly, calorimetric measurements can be systematically applied to obtain the same type of information. 

The contributions of steroids functional groups to the differential entropy of adsorption from ethanol-water eluents ( — AH i) on silica with bonded octadecylsilyl groups... 

S, and H, are the total or integral entropy and heat content of the one-component system of adsorbed molecules. An isosteric calculation [Eqs. (52) and (53)] from neighboring adsorption isotherms gives the differential entropy and heat content, (dS,/dnf)a.r and (dHJdnfja,t-The integral entropy is the quantity of direct statistical mechanical significance, being related to the number of possible quantum states of We adopt the H, and 3C notation of Everett (86), for clarity. 

Since through Eq. (23) the adsorption potential A is related to the Gibbs fiee energy the differential entropy and the differential enthalpy for a given adsorbate can be expressed as follows ... 

The first attempts to predict macroscopic properties such as Henry constants, initial isosteric heats of adsorption, or changes in the standard differential entropies for noble gases, H2, N2, O2, CO, H2O, NH3, CO2, n-alkanes up to Cg, ethylene, acetylene, and benzene in silicalite were performed by Kiselev and coworkers about 20 years ago.224-227 These workers used potential param-... 

The molar differential entropy of adsorption resulting from the transfer of dn moles of the adsorbate from gas to the adsorbed phase likewise can be represented as... 

This is the differential entropy of adsorption per molecule, and the corresponding value per mole is obtained by multiplying by L. This will be denoted A8,... 

In addition Jellinek and Iwakl studied the adsorption of water vapor on these block copolymer coatings in the form of films. The magnitudes of the Isosteric heats and the molar differential entropies reflected correctly the abhesion data for the block-copolymer of different siloxane block chain length and content. 

Thus from an adsorption isotherm and its temperature variation, one can calculate either the differential or the integral entropy of adsorption as a function of surface coverage. The former probably has the greater direct physical meaning, but the latter is the quantity usually first obtained in a statistical thermodynamic adsorption model. 

Also, the differential molar entropy of adsorption, AJ, is defined as... 

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